Dualities between Laplace Transform and Some Useful Integral Transforms

Abstract

Integral transforms have wide applications in the various disciplines of engineering and science to solve the problems of heat transfer, springs, mixing problems, electrical networks, bending of beams, carbon dating problems, Newton’s second law of motion, signal processing, exponential growth and decay problems. In this paper, we will discuss the dualities between Laplace transform and some useful integral transforms namely Kamal transform, Elzaki transform, Aboodh transform, Sumudu transform, Mahgoub (Laplace-Carson) transform, Mohand transform and Sawi transform. To visualize the importance of dualities between Laplace transform and mention integral transforms, we give tabular presentation of the integral transforms (Kamal transform, Elzaki transform, Aboodh transform, Sumudu transform, Mahgoub transform, Mohand transform and Sawi transform) of mostly used basic functions by using mention dualities relations. Results show that the mention integral transforms are strongly related with Laplace transform.